4. The bathtub model of unemployment is: Et+ U: = L UI+l = gEt JFU: 3 {a} (1 point} The steadystate unemployment rate in the bathtub model is given by u = _ s + f . Suppose s = 0.02 and f = 0.3. What. is the unemployment rate? [b] (1 point} Suppose that f increases to 0.4. What is the new unemployment rate? {1:} (2 points) Without using math, briey explain why the change in the unemploy ment rate between parts {a} and (b) makes sense. [d] (2 points) Mathematically demonstrate how it changes as f changes by nding @ 3f and explaining if the derivative is positive or negative. {e} (1 point} Are your answers to parts {d} and {e} consistent? Why or why not